Voltage controlled crystal oscillators (VCXO) are well known in the art and generally comprise a voltage tunable resonator having a crystal unit and a voltage variable capacitance coupled across a sustaining stage such as an appropriately biased transistor amplifier.
One such VCXO is disclosed in U.S. Pat. No. 3,571,754 issued to Daniel J. Healey III and the present inventor on Mar. 23, 1971. As disclosed therein, the oscillator employs a high Q composite resonator that consists of a network containing a quartz crystal unit, in combination with capacitors, inductors and varactor (voltage variable capacitance) diodes. Oscillator operation occurs at the parallel resonant frequency of the resonator, designed specifically to exhibit a near linear relationship between resonant frequency and applied varactor tuning voltage. In addition to the desired (high Q) resonance, the composite resonator exhibits two undesired resonances occuring typically at 95% and 120% of the desired frequency, and use of a spurious suppression network is required to eliminate the possibility of oscillator operation at the undesired resonances. The particular circuit configuration was a direct result of a requirement for relative wide tuning range (0.25% typical). Varactor diode operation over a tuning voltage range resulting in 1.5 to 1 maximum usable diode reactance ratio defines oscillator frequency sensitivity to circuit component change. For example, a VCXO tuning 2500 PPM using 100 pF effective tuning diode capacitance operated at 5 to 14 volts tuning voltage will have a worst case frequency sensitivity to capacitance change (at the varactor diode circuit node) of approximately 150 PPM/pF. Because of this fact, it is usually necessary to temperature control and hermetically seal the oscillator circuit. In currently utilized applications for narrow deviation VCXO's where much lower tuning range is required (250 PPM typical), a wide deviation VCXO design is often utilized with tuning diode operation over a much smaller applied tuning voltage. The result of this is needless use of very much reduced diode reactance variation (10% or less), with no improvement in oscillator sensitivity to circuit element change, compared to a VCXO having 10 times larger tuning capability.
A narrow deviation VCXO developed by the present inventor and Rafi Arekelian is described in U.S. Pat. No. 4,134,085 issued on Jan. 9, 1979. In this VCXO circuit, a linear tuning characteristic is achieved using the large available tuning diode reactance variation (approximately 1.5 to 1 for 5 to 14 volts) resulting in much reduced oscillator output signal frequency sensitivity to circuit component reactance changes. In addition this circuit utilizes a reduced number of critical components, and does not require use of a spurious suppression network. While a spurious resonance exists for the composite resonator 10 shown in U.S. Pat. No. 4,134,085, it is lossier than the desired resonance and of little concern. The composite resonator is located in the base circuit of the sustaining stage transistor and operates as a parallel resonant circuit. Because of this, the oscillator circuit disclosed in U.S. Pat. No. 4,134,085 exhibits a noise floor typically 15-20 dB higher than the circuit disclosed and claimed herein.
The spectral density of the fractional phase fluctuations of the output signal in the oscillator circuits described above can be expressed as: EQU S.delta..phi.(f)=2[(Ko/.sub.f +K1)(fo/2Qf).sup.2 +K2]
where:
Ko=oscillator open loop flicker noise constant PA0 K1=oscillator open loop white noise constant PA0 fo=carrier frequency PA0 Q=effective (loaded) composite resonator Q PA0 K2="residual" oscillator white noise constant for oscillator noise sources not subject to band limiting by the composite resonator frequency selectivity characteristic
(K2 can have a 1/f component).
FIG. 1 shows (in general form) the resulting oscillator short-term stability. .zeta.(f)=10 log (S.delta..phi.(f)/2) and is defined as the ratio of the power in one phase noise sideband, on a per Hertz bandwidth spectral density basis, to the total signal power, at Fourier frequency f from the carrier. As shown in FIG. 1, there is a conversion of oscillator (open loop) white phase noise to white frequency noise (20 dB/decade), and flicker phase noise to flicker frequency noise (30 dB/decade) at frequencies less than the oscillator composite resonator half-bandwidth. This is the result, in the closed loop oscillator, of the conversion of (open loop) oscillator phase uncertainty to (closed loop) frequency uncertainty due to the requirement in the oscillator, of maintenance of 2.pi.n radians closed loop phase shift. The degree of phase to frequency conversion is determined by the oscillator composite resonator phase slope d.phi./df=2Q/f.sub.o.
At frequencies in excess of the oscillator resonator half bandwidth, the noise `floor` level is simply 10 log K2. K2 represents the residual noise of the (open loop) oscillator sustaining stage and can be calculated for the aforementioned circuits using the overall composite resonator out-of-band impedance value appearing between the sustaining stage input transistor junction terminals.
FIG. 2 shows the basic (white) noise sources in the transistor. For further detail regarding such noise sources and related formulae, reference should be made to an article by Van Der Ziel entitled "Noise in Solid State Devices and Lasers", which appeared in the Proceedings of the IEEE, Vol. 58, No. 8, August, 1970, pp 1178-1206. For both the circuits, the values of the impedance of the composite resonator `out-of-band` (at frequencies offset from the carrier in excess of the resonator half bandwidth), are relatively small. As a result, the emitter shot noise generator plays a dominant role in establishing the oscillator output signal noise floor. For the circuits disclosed above, K2 in the range 10.sup.-15 to 10.sup.-16 rad.sup.2 /Hz is typical for crystal unit dissipations in the range 100 to 300 microwatts.